The top executive at Fort Worth-based American Airlines Group is urging Arizona Gov. Jan Brewer to veto a bill that would allow businesses to refuse service on religious grounds, a measure that opponents say is meant to allow discrimination against gays.

The measure, which passed last week, prompted tourists to cancel reservations and companies to say they would move if it became law. The bill threatens to reverse an economic recovery in a state hit hard by the housing crash, opponents said, and cement a reputation fostered by a 2010 anti-immigration law and a fight in the 1990s over celebrating the Martin Luther King Jr. holiday.

“There is genuine concern throughout the business community that this bill, if signed into law, would jeopardize all that has been accomplished so far,” Doug Parker, American’s CEO, wrote in a letter to Brewer on Monday. He said it could reduce the desire of companies to come to the state and could repel convention business.

“Our economy thrives best when the doors of commerce are open to all,” he wrote.

Parker was CEO of Phoenix-based US Airways Group before it merged with AMR Corp. to form American Airlines Group. The newly merged American, created in December, has promised to keep the city as a flight hub for three years.

Asked Saturday whether she plans to sign the bill this week, Brewer said she needed to review it.

“I don’t have to make a decision until next Friday, so I’ve got plenty of time,” Brewer said at a National Governors Association meeting in Washington.

Brewer also declined to say whether next year’s Super Bowl could move from Arizona if the bill takes effect.

Arizona business groups said publicity surrounding the bill’s quick trip through the Republican-controlled Legislature prompted firms to reconsider their commitment to the state.

“This legislation will likely have profound negative effects on our business community for years to come,” wrote James Lundy, chairman of the Greater Phoenix Economic Council, and Barry Broome, its chief executive officer, in a letter to Brewer.

“With major events approaching in the coming year, including Super Bowl XLIX, Arizona will be the center of the world’s stage,” they said. “This legislation has the potential of subjecting the Super Bowl, and major events surrounding it, to the threats of boycotts.”

A National Football League spokesman said the organization is following the issue.